Question

Find the number of positive numbers less than 2020, which can be written as the sum of five consecutive positive numbers.

Answer 1

Integers*?

Let $n$ be the smallest of these five consecutive integers. Then the sum of the five consecutive integers is $\frac{5(2n+4)}{2}=5n+10,$ so we seek the largest positive integer $n$ such that $5n+10<2020.$ Solving this inequality, we find that $n<402,$ so there are $\boxed{401}$ such positive integers.